Have you run software update and repaired premissions?
Was FCPX installed before or after FCP7?
FCP7 and the other FCS3 apps should be located in a folder in Applications if you're going to have them coexist with FCPX. If you had FCS installed prior to downloading FCPX, that relocation is done automatically. But you could also do it manually.
If you haven't sen it, here is Apple's best installation practices.